Many applications in computer graphics and related fields can benefit
from automatic simplification of complex polygonal surface models.
Applications are often confronted with either very densely
over-sampled surfaces or models too complex for the limited available
hardware capacity. An effective algorithm for rapidly producing
high-quality approximations of the original model is a valuable tool
for managing data complexity.

In this dissertation, I present my simplification algorithm, based on
iterative vertex pair contraction. This technique provides an
effective compromise between the fastest algorithms, which often
produce poor quality results, and the highest-quality algorithms,
which are generally very slow. For example, a 1000 face approximation
of a 100,000 face model can be produced in about 10 seconds on a
PentiumPro 200. The algorithm can simplify both the geometry and
topology of manifold as well as non-manifold surfaces. In addition to
producing single approximations, my algorithm can also be used to
generate multiresolution representations such as progressive meshes
and vertex hierarchies for view-dependent refinement.

The foundation of my simplification algorithm, is the quadric error
metric which I have developed. It provides a useful and economical
characterization of local surface shape, and I have proven a direct
mathematical connection between the quadric metric and surface
curvature. A generalized form of this metric can accommodate surfaces
with material properties, such as RGB color or texture coordinates.

I have also developed a closely related technique for constructing a
hierarchy of well-defined surface regions composed of disjoint sets of
faces. This algorithm involves applying a dual form of my
simplification algorithm to the dual graph of the input surface. The
resulting structure is a hierarchy of face clusters which is an
effective multiresolution representation for applications such as
radiosity.